Similarity & Proportions

Front

What is the definition of similar triangles?

Back

Triangles that have the same shape but may have different sizes. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

What is the SAS similarity criterion?

Back

If two triangles have one angle equal and the sides including that angle are in proportion, then the triangles are similar.

Front

What is the SSS similarity criterion?

Back

If the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

If triangle ABC is similar to triangle DEF, and the lengths of AB and DE are 4 and 8 respectively, what is the ratio of their corresponding sides?

Back

1:2

Front

Solve for x: If triangle ABC is similar to triangle DEF, and the lengths of AB = 5, DE = x, and AC = 10, DF = 20, find x.

Back

x = 10

Front

What is the definition of proportional sides in similar triangles?

Back

The lengths of corresponding sides of similar triangles are in the same ratio.

Front

If two triangles are similar, how do you find the length of a missing side?

Back

Use the ratio of the lengths of the corresponding sides to set up a proportion and solve for the missing length.

Front

Solve for x: If triangle ABC is similar to triangle DEF, and the lengths of AB = 6, DE = 3, and AC = x, DF = 9, find x.

Back

x = 4.5

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

If triangle GHI is similar to triangle JKL, and the lengths of GH = 12, JK = 6, find the ratio of their areas.

Back

The ratio of their areas is (12/6)² = 4:1.